Simplifying XML Schema: Single-type approximations of regular tree languages

XML Schema Definitions (XSDs) can be adequately abstracted by the single-type regular tree languages. It is well known that these form a strict subclass of the robust class of regular unranked tree languages. Sadly, in this respect, XSDs are not closed under the basic operations of union and set difference, complicating important tasks in schema integration and evolution. The purpose of this paper is to investigate how the union and difference of two XSDs can be approximated within the framework of single-type regular tree languages. We consider both optimal lower and upper approximations. We also address the more general question of how to approximate an arbitrary regular tree language by an XSD and consider the complexity of associated decision problems.

► XSDs are not closed under union and set difference. ► Approximations of those operations as single-type tree automata are presented. ► Both lower and upper approximations are studied. ► Complexity analysis is carried out in full detail.